CP violation in B meson decays

Transcription

1 CP violation in B meson decays (INFN) Outline of the lectures i. Indirect search for CP violation Introduction to CP violation CP violation in the Standard Model: the CKM matrix The classic Unitarity Triangle Analysis ii. Direct search for CP violation Introduction to CP violation in meson decays CP violating B decays: CP asymmetries UTA in the late B factory era iii. Beyond the Standard Model: New Physics in DB = transitions Model independent parameterization Minimal Flavour Violation and the UUT MSSM with flavour changing squark mass insertions

2 Discrete symmetries P Parity T Time reversal C Charge conjugation Classically p -p t -t e -e QFT a(p,s) a( p,s) b(p,s) b( p,s) a(p,s) a( p, s) b(p,s) b( p, s) a(p,s) b(p,s) b(p,s) a(p,s) Fundamental symmetries related to intrinsic ambiguities Left right convention ("the looking glass") Arrow of time Charge sign (particle antiparticle) convention Are these symmetries conserved by the interactions? QED U(1) QCD SU(3) Weak SU()L SM SU()L U(1)Y C Yes Yes P Yes Yes T Yes Yes CP Yes Yes* CPT Yes Yes No No Yes Yes Yes No No No No Yes Page

3 CP violation: why was interestings 5 years ago? The CP violation mechanism of the SM is very peculiar CP symmetry is explicitly broken by the Yukawa couplings CP is not an approximate symmetry of the model. CP violation is suppressed by mixing angles, but there are O(1) effects A single source of CP violation in the weak interactions of quarks. All CP-odd observables are correlated Three-generations unitarity: CP-violating parameters from the measurement of CP-conserving observables All these features need(ed) experimental confirmation Page 3

4 C S (x,t) P (x,t) Vm (x,t) Am (x,t) S + (x,t) P + (x,t) Vm+ (x,t) Am+ (x,t) LL= i ci Qi h.c.: P S + ( x,t) P + ( x,t) Vm + ( x,t) Am + ( x,t) T S + (x, t) P + (x, t) Vm + (x, t) Am + (x, t) CP Qi CP =Q LLint = c A + CP S ( x,t) P ( x,t) Vm ( x,t) Am + ( x,t) * i i * CPT S ( x, t) P ( x, t) Vm ( x, t) Am (x,t) then c i c CP - V c A V + + * + L P Lint P = c A V c A V * + L CP Lint CP = c A V c A V + c 0 P * c c CP Free Lagrangians conserve C, P and T separately Gauge interactions conserve CP (couplings are real) Other interactions violate CP if the couplings are complex Page 4

5 CP violation in the Standard Model LL LL SM =L L kin+gauge L L Higgs L L Yukawa =QL Y u u R Q L Y d d R L L Y l l R LL Y R h.c. Yukawa + T CP QL Y d d R CP =d R Y d Q L d R Y d QL unless Y d is real Global symmetry: U 3 Q U 3 u U 3 d U 1 B L R R Y Counting the physical parameters in the quark sector n Y u,y d n n 3 n n 1 n n 1 =9 moduli = n n 3 angles in a unitary matrix phases in a unitary matrix 1=1 phase Page 5

6 Cabibbo-Kobayashi-Maskawa matrix Mass eigenstates u L,R L,R u,d L u,d u L, R=U u ' diag M u,d =U M' U u,d R d L,R u L d L, R =U d ' L, R d V CKM U U L g LL cc= u L V CKM d L W h.c. VCKM, 3 3 unitary matrix with 4 free parameters: (quark masses take away the remaining 6) 3 angles: 1 phase [3(3+1)/-((3)-1)]: Page 6

7 The standard parameterization -i c 13 0 s13 e V CKM 0 c 3 s i 0 s 3 c3 s 13 e 0 c 13 Maiani Chau, Keung Harari, Leurer Fritzsch, Plankl Botella, Chao V ud V us V ub V CKM = V cd V cs V cb = V td V ts V tb c1 c 13 s 1 c 13 s1 c 3 c1 s 3 s13 e c 1 s 1 0 s 1 c s1 s 3 c 1 c 3 s13 e i i s 13 e i c 1 c3 s1 s 3 s 13 e c 1 s 3 s 1 c 3 s 13 e i - i s 3 c 13 c13 c 3 Page 7

8 The Wolfenstein-Buras parametrization s1~0., A s 3, A i s 13 e 3 -i V td = A 1 i with 1, 1 3 V CKM = 1 A i 1 3 A 1 i A Main features: 3 A 1 Wolfenstein, '83 Buras et al., '94 4 O Vus ~ O(l7) Vcb ~ O(l8) the unitarity triangle is exact! Page 8

9 Unitarity relations CKM V CKM V =1 V ki V kj = ij Unitarity 9 constraints 6 triangular relations k Only two triangles have all sides with the same length of O(l ) ub td cb ts tb tb V ud V V cd V V td V =0 V ud V V us V V ub V =0 Page 9

10 CP physics CP physics Triangles sides angles VV* a b g arg * V td V tb V ud V * ub, arg * V cd V cb * V td V tb * V ud V ub, arg * V cd V cb CP violation is proportional to the Jarlskog invariant J = Im VijVklVil*Vkj* Page 10

11 Standard Analysis of the Unitarity Triangle / 1 / = V ub /V cb Bs 6 C m Bs f A [ 1 ]= m B 6 circle (0,0) d 4 C B K [ 1 A C tt C tc C cc ]= K mb d mb s [ 1 ]= 1 1 mb d mb s =sin A J / K S t CP circle (1,0) hyperbola disc (1,0) 4 angle Page 11

12 Progress of the UT analysis Page 1

13 Outcome of the sides UT Analysis =0.197±0.034 [0.17, % =0.397±0.05 [0.349, % The triumph of Lattice QCD Page 13

14 Predictions from the UT fit: Dms Dm CDF s (1.5.6) ps 1 = ( ) ps 1 Page 14

15 Testing the model: Direct vs Indirect circa 005 sides only Spectacular agreement between direct and indirect measurements sin sides =0.73±0.044 sin ind =0.79±0.04 sin dir =0.75±0.037 sin =0.78±0.08 Page 15

16 15 years of sin b Page 16

17 006: Is the test already interesting? Tension between Vub/Vcb and the new measurement sin New Physics or Vub inclusive? exclusive inclusive Page 17

18 CP violation in meson decays QM description of two CP conjugated neutral mesons: CP M = M a t M b t M : d a a i i =H = m dt b b a b Energy eigenstates: M ± ± p M ±q M i ± H H Eigenvalues: ± =m ± ± = H * * H 1 m1 i 1 q Eigenvectors: = = p m i / H 1 Page 18

19 Time evolution 1 -i t -i t M t = e M+ e M - 1 p -i t -i t M t = e M- e M + q q M t =f + t M f - t M p p M t =f + t M f - t M q + where f ± t e - i + t 1±e- i t Let's also introduce the amplitudes for M, M f, f where CP f = f Af f H int M Af f H int M Af f H int M Af f H int M B t [ B t ] f [f ] f [f ] H int B t [ B t ] Page 19

20 Master formulae M t f Af M t f Af [ [ q Af q Af * f + t p A f - t Re f + t f - t p A f f p Af p Af * f + t q A f - t Re f + t f - t q A f f ] ] 1 t /t cos m t f ± t = 4 1 e ± e 1 * t / t f + t f - t = 1 e i e sin m t 4 The mother of all CP odd observables: the time dependent CP asymmetry M t f M t f a t M t f M t f f CP Page 0

21 How do we observe CP violation? Case n. 1: CP violation in the decay No mixing: Dm=DG=0 acp is time independent f CP f + t =1, f - t =0 f M a f M Af Af = 0 Af Af Af Af acp in this case is called simply CP asymmetry acp 0 iff Af contains amps with different weak and strong phases Af = A1 e i 1 i 1 e A e i e i Af = A1 e - i 1 i 1 e A e -i e i f acp ~sin 1 sin 1 Page 1

22 Case n. : CP violation in the mixing e.g. semileptonic decay M l- X ("wrong sign lepton") no direct CP violation Af = Af (CPT) acp is time independent f M q M t l X A SL f - t p - f M p M t l X ASL f - t q q / p 1 a = =Im 0 q /p 1 4 m1 1 q / p SL CP Page

23 Case n. 3: CP violation in the interference between mixing and decay Simplifying assumptions: i M ~0, q / p~e i Af / Af = e M f M f D 1 1 * 1±cos m t, f t f t = i sin m t + 1 f acp t = cos m t sin M D sin m t 1 1 f ± t = Decay into a CP eigenstate with 1 amplitude: CP f = ± f ±1 afcp t = sin M D sin m t M D is a physical observable, but M and D are not Page 3

24 CP violation in B decays The phenomenology of CP violation in K and B decays is quite different S K : m m ~ m~ ~ m~ B d : m m m m~ To our purpose, the main consequence is the expectation that 1-3 a =Im ~10 m1 m SL CP Perturbative estimates give asl 10 4 due to an accidental cancellation of the leading phase between G1 and m1 CP violation through mixing is much smaller than the others: better look for other CP violating mechanisms it is generally safe to neglect its contribution Page 4

25 a CP t in B J / K S Decay into a CP eigenstate: CP J / K S = J / K S c b c B c J / s s b c d KS d b B d Two amplitudes enter A, but with the same weak phase * * A J / V cb V cs T V ub V us P A T b s c b s c c D =0 c Page 5

26 The CP aymmetry in this mode measures the phase of the mixing amplitude: q / p a J / K S CP V td V *tb * V td V tb =e - i M = t =sin sin m t Mixing phase measured with small hadronic uncertainties: ~ % sin =0.687±0.03 BaBar + Belle further determinations (including the indirect one) test the CP violation mechanism in B decays Page 6

27 + a CP t in B - Another CP eigenstate: CP + - = + - d b u B d + u u d u d - b d Again two amplitudes enter A, but now... A * + * 3 b B 3 V ub V ud T V cb V cd P A i T A P - b d u b d u u D = u Page 7

28 Neglecting P : D = a + CP - t = sin sin m t =sin sin m t If P cannot be neglected, one measures i i 1 e P /T sin eff =Im e sin -i 1 e P /T At the same time, CP violation in the decay is expected The extraction of a from acp(t) requires the knowledge of the ratio P / T involving several hadronic amplitudes The experimental situation is still unclear at present: 0.09±0.15±0.04 BaBar C = 0.56±0.1±0.06 Belle ±0.17±0.03 S = 0.67±0.16± Page 8

29 b sss), hadronic amplitudes are With few exceptions (b ccs, the open problem in the extraction of the UT angles from acp(t) I. Compute the relevant hadronic amplitudes Main theoretical tool: Factorization derived from QCD at 1 loops for mb models for the mb suppressed terms required by the data in many cases: th. error? Extension to all order in as: SCET II. Devise strategies to get (some of) the amplitudes from the data a: Gronau London,... g: GLW, ADS,... rely on flavour symmetries to some extent: th. error? often experimentally challenging Page 9

30 Summary #1 We recalled how CP violation appears in the SM and how to study it in (B) meson decays We discussed how the SM CPV mechanism was tested with the early B-factory results Other CKM angles can be (and have been) measured: do we learn something about the physics beyond the SM? The perspective changes... Page 30

31 The UT analysis in the late B-factory era _ ACP(b ccs) (J/ K,...) sin cos sin sin( ) ACP(b sss, dds) ( K, K,...) ACP(b ddd, uud) (, ) BR(b cud, cus) (DK, D ) sin BR(B ) Vub BR(B )/BR(B ) Vtd Page 31

32 Sinb from b -> s modes Still systematically smaller than sinb from b -> ccs (?) Theoretically-motivated large NP contributions in SUSY-GUT's Page 3

33 a from rr/rp and SU() flavour symmetry Parametrization of the rr (pp) amplitudes (neglecting EWP) i Gronau, London, PRL65 (1990) 3381 i P = T e P e 1 i 0 i 6 unknowns: T, Tc, P, P, C, a A = e T T c e 6 observables: 3xBRave, C+-, S+-, C00 1 A00= A 0 A 0 + time-dependent Dalitz plot study of ( rp ) A C Snyder, Quinn, PRD48 (1993) 139 [83,111]o U 95% Prob. Page 33

34 g from B D(*)K no penguins four different flavours many modes XCPES=Ks p, Ks r, p+ p-,... XCPNES=K+ p-, K+* p-,... K+* K-, p+ r-,... Charged B: CP violation in the decay g + GGSZ: Dalitz plot analysis of D0 3-body modes, ex. Ksp+p- Neutral B: CP violation in the interference between mixing and decay sin(b+g) Page 34

35 r B D K = A B D K A B D K (65.0±0)o U (-115.0±0)o Page 35

36 and : all together =0.193±0.09 =0.355±0.019 Page 36

37 Sides vs Angles No angles: Vub/Vcb, Δmd, Δms, K Angles only: sin, cos, sin, the parameter determination era ends the precision/new physics test era begins Page 37

38 CP violation: why is interesting today? Surprisingly enough, the SM paradigm of CP violation is confirmed at least for s d and b d decays Flavour and CP violation are likely determined by the structure of the SM Yukawa couplings (Minimal Flavour Violation?) The same CP-violating parameter is consistently determined from CP-odd and CP-even observables as expected in the SM SM correlations among CP-odd observables still to be fully explored (already some puzzles in b -> s transitions?) Redundancy and accuracy are the keys to New Physics Page 38

39 Exploiting the flavour problem The SM is an effective theory valid up to some scale L = LSM + Sk=1 C Q /L (k+4) Gauge hierarchy problem: L 1 TeV Flavour physics: L TeV L k Tension between new physics scales 1. Large effects from NP in loops are possible and generically expected in untested sectors Flavour physics has a big potential for the indirect search of NP Page 39

40 . New particles produced at the LHC cannot have generic flavour properties Flavour Physics: The New Physics Genome Project b) e tan derat e tanb) o m ( g lar GRA m SU SUGRA ( UT with nr m G Y USY S U )S tive S SU(5 Effec exchange n ns avito ensio KK grextra dim sions n rge ime ions s in la xtra d s rmion niversal e t ra di men e f it l x U Sp e l rs a Unive ity nitar Bd u violation s cay CP B de dent ls epen Rare d signa r e Tim Ot he DNA identification of new physics M. Hazumi, 1st Workshop Flavour in the LHC era In a given NP framework, flavour- and CP-violating observables provide insights on the structure of NP (for ex.: Soft SUSY-breaking terms in the MSSM) Complementary to NP searches at the LHC Page 40

41 Checking the Unitarity Clock (1) 3-generations unitarity Assumptions: () no new physics in tree-level processes Using only tree-level: and Vub/Vcb. Results: r = h = sinb = = (65±0)o ( 115±0)o a = (87±17)o ( 46±17)o Any model of new physics must satisfy these constraints UTfit coll., hep-ph/ ; Botella et al., hep-ph/ Page 41

42 The Brute Force Strategy 1. Add most general NP to all sectors. Use all available info 3. Constrain simultaneously and NP parameters Only possible thanks to the measurements of CKM angles! Botella et al., hep-ph/050133; Agashe et al., hep-ph/ ; UTfit coll., hep-ph/ Previous attempts: Ciuchini et al., hep-ph/ ; CKMfitter group, hep-ph/ ; Ligeti, hep-ph/ Page 4

43 General Parameterizion of the Amplitudes B q Bq mixing: AB = A d K K mixing: mq =C q mq SM Bq e i q A e Im AK =C Im A SM NP Bq SM K i q NP B d =C q e i q q SM AB q 1, ACP J / K S =sin B, ASL =Im AB d d (3) assuming a Penguin-like NP, the only effect on the pp amplitudes is an additional weak phase fp Page 43

44 The UT in the presence of NP Page 44

45 Using:, md, Vub/Vcb, sin Page 45

46 Using:, md, Vub/Vcb, sin SM+NP1 NP+NP3 NP3 NP1 NP SM Page 46

47 Using:, md, Vub/Vcb, sin,, ASL SM NP NP SM Page 47

48 Using:, md, Vub/Vcb, sin,, ASL ms, ACH, DGq/Gq SM Page 48

49 Putting all together... UTfit coll., hep-ph/ Page 49

50 Hints for Model Building Two classes of NP models are suggested by the UT fit: 1. Models with no new sources of flavour and CP violation Minimal Flavour Violation. Models with large new sources of flavour and CP violation confined to b s transitions Page 50

51 1. Minimal Flavour Violation Gabrielli, Giudice, NPB433 D'Ambrosio et al., NPB645 1) No new source of flavour and CP violation NP contributions governed by SM Yukawa couplings Ex.: Constrained MSSM (MSUGRA), Universal Extra Dim. NP only modifies SM top contribution to FCNC & CPV a) One Higgs or small/moderate tan No new operators Full correlations among K and B decays b) Large tan New operators Less correlations among K and B decays Page 51

52 The Universal Unitarity Triangle Buras et al., PLB500 Angle measurements + Dmd/Dms unaffected by NP in MFV valid in any MFV model for any value of tan accuracy comparable to SM Page 5

53 Constraints on the MFV effective scale D'Ambrosio et al., NPB645 MFV models with one Higgs doublet or low/moderate tan : Universal NP effect in the DF= Inami-Lim function of the top S 0 x t S 0 x t S 0, S 0 =O 4 We can bound the NP scale 0, 0 ~.4 TeV L: L > 5.7 prob. Page 53

54 Higgs doublets + large tanb: terms proportional to the bottom Yukawa coupling are enhanced and cannot be neglected any more B 0 S S K 0 Could give information on the tanb regime unfortunately none at present correlation coefficient = 0.5 L > 5. prob. Page 54

55 .Flavour and CPV NP in b -> s transitions natural in any flavour models given the strong breaking of family SU(3) Pomarol, Tommasini; Barbieri, Dvali, Hall; Barbieri, Hall; Barbieri, Hall, Romanino; Berezhiani, Rossi; Masiero, Piai, Romanino, Silvestrini; hinted at by s in SUSY-GUTs Baek, Goto, Okada, Okumura; Moroi; Akama, Kiyo, Komine, Moroi; Chang, Masiero, Murayama; Hisano, Shimizu; Goto, Okada, Shimizu, Shindou, Tanaka; already some experimental hints in the time-dependent CP asymmetries Let's consider the SUSY option

56 MSSM + generic soft SUSY-breaking terms Useful tool: the mass-insertion approximation SuperCKM basis + perturbative smass diagonalization expansion parameters: ij AB q q Mij AB m All flavour-changing NP effects in the squark propagators q ij AB i A q q={u, d }, A, B ={L, R} i, j ={1,,3} j B q FCNC and CP violation impose model-independent bounds on the 's NB: only dominant gluino contributions are considered

57 Constraints on the 's gluinos contribute to rare decays only through (chromo)magnetic penguins (electro)penguin operators are suppressed Bertolini et al., NPB353; Gabbiani et al., NPB477; Buras, Romanino, L.S., NPB50 very strong constraints from the combination of b s and b s l+ l- (both dominated by C7eff) MC et al; Hiller, PRD69; Gambino, Haisch, Misiak, PRL94 Updated results for mgl = msq = - = 350 GeV, tan = 10 Page 57

58 Re ( d3)ab RY vs Im ( d3)ab AB = RR PR EL IM IN A AB = LL AB = LR b s only b s ll only All constraints AB = RL Page 58

59 SX X = Kw X = Kh' PR EL I M IN A RY X = Kf vs Im ( d3)rl X = Kp Page 59

60 The impact of Dms DmsCDF = ( ) ps 1 MC, Silvestrini hep-ph/ Good news for LHC: large effect in B -> J/y f Page 60

61 Conclusions # The UT is SM-like. Generic NP in any DF= transitions are constrained by present data + lattice QCD results UT fit results point to either no new physics in s d and b d DF= transitions or models with MFV The CKM matrix determination for MFV models is competitive with the SM one, improving predictions for rare decays. Data already probe scales of several TeVs Still ample room for NP in b s transitions after the CDF measurement. B -> J/y f is the golden mode for LHC Strong complementarity between direct searches of NP at the LHC and precision flavour physics Page 61